It is my understanding from my own experiences that in order to make up "matching Pairs" of tubes you need one of these expensive antiquated machines capable of reading the valves values. So many ins, so many types of valves and then to refer to the books.

I have made tube matching ( = selection of equal pairs) without any tester by simply using fixed anode and screen power supply and adjustable G1 negative suppy. I just connect these to the tube socket by jumper wires.

Then I adjust the anode current to typical operating value by means of G1 voltage and simply put all the required tubes in turn in this test installation and take the anode current readings.

I have made tube matching ( = selection of equal pairs) without any tester by simply using fixed anode and screen power supply and adjustable G1 negative suppy. I just connect these to the tube socket by jumper wires.

Then I adjust the anode current to typical operating value by means of G1 voltage and simply put all the required tubes in turn in this test installation and take the anode current readings.

Even the Gm could be analyzed/matched with this simple system.

This way is probably the easiest and best way to go. If you have lots of time, you can slowly adjust G1 voltage and graph it along with plate current readings. Then you can match up graphs / plots of your group of tubes and get excellent matched pairs / quads, etc.
I have done it this way for years... I usually buy 26-30 tubes of a particular type and manufacturer burn them in for 24 hours and then do the plots of G1 voltage vs. plate current. With this many tubes I usually get several matched quads, several pairs; I have even got an octet once. Most tubes will match; I might get 2 tubes left over that don't match very good with the rest.
And I am talking tight matching... like to within 1%, 2% at most.
Traditionally, matching has meant matching for transconductance only. Groove Tubes changed this for the better.... They matched for both transconductance and current... This is the way to go. With the above equipment you will be able to do this.
Basically what you will need is 2 power supplies... B+ and a negative supply for the G1 voltage. If you want to get fancy, make the voltages regulated. If you want to get real fancy, make the screen (G2) voltage variable also...
And if you want to achieve "tube guru" status... Make the tester all automatic; let it do all the work... You are on your own on that one though....
Daniel